The \(\mathbb {I}_{x}\)  and \(\mathbb {I}_{y}\)  are identity matrices
for the basis along \(x\)  and \(y\)  directions of the lattice. \(\sigma _{x,y,z}\) 
are Pauli matrices and \(\sigma _{-}=(\sigma _{x}-i\sigma _{y})/2\) . \(m,n\in \mathbb {Z}\) 
are unit cell indices along the two spatial dimensions. \(\Delta \) 
and \(J_{1,2}\)  describe hopping amplitudes between nearest neighbor
cells along the \(x\)  and \(y\)  directions. \(\mu \)  characterizes the strength
of an onsite potential bias. Gain and loss are introduced to make
the system non-Hermitian by setting \(\mu =u+iv\) , with \(u,v\in \mathbb {R}\) 
and \(v\ne 0\) . The Floquet operator of the system takes the form \({\cal U}=e^{-i\frac{1}{2}{\cal H}_{1}}e^{-i\frac{1}{2}{\cal H}_{2}}\) ,
whose spectrum under the OBC features fourfold degenerate topological
corner modes at zero and \(\pi \)  quasienergies. The numbers of these
corner modes \(n_{0}\)  and \(n_{\pi }\)  are related to a pair of bulk
topological winding numbers \(\nu _{0}\)  and \(\nu _{\pi }\)  of \({\cal U}\)  (see Appendix  for their definitions)
through a bulk-corner correspondence relation \((n_{0},n_{\pi })=4(|\nu _{0}|,|\nu _{\pi }|)\)  [1]}.
The fourfold degeneracy of Floquet
corner modes at the quasienergies \(E=0,\pi \)  is protected by the CS
\(\Gamma =\sigma _{z}\otimes \sigma _{y}\)  of the two-dimensional system
described by \({\cal U}\)  [1]}.
